Pith Number

pith:DZ4HIVPH

pith:2024:DZ4HIVPHLYFERYP63GGRLYLBYP

not attested not anchored not stored refs pending

The Frankl-Pach upper bound is not tight for any uniformity

Chi Hoi Yip, Gennian Ge, Shengtong Zhang, Xiaochen Zhao, Zixiang Xu

arxiv:2412.11901 v2 · 2024-12-16 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DZ4HIVPHLYFERYP63GGRLYLBYP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Uniform set systems with small VC-dimension

Receipt and verification

First computed	2026-06-09T02:08:27.830600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e787455e75e0a48e1fed98d15e161c3f7bd48294ca813c0df39f4cbf37f00d0

Aliases

arxiv: 2412.11901 · arxiv_version: 2412.11901v2 · doi: 10.48550/arxiv.2412.11901 · pith_short_12: DZ4HIVPHLYFE · pith_short_16: DZ4HIVPHLYFERYP6 · pith_short_8: DZ4HIVPH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DZ4HIVPHLYFERYP63GGRLYLBYP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 1e787455e75e0a48e1fed98d15e161c3f7bd48294ca813c0df39f4cbf37f00d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6288b61349a88b6c97a43e07e59a5888f54c480575564f64d9eea709891579eb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-16T15:46:31Z",
    "title_canon_sha256": "c70d2a9c4958fb3752492df156b77bfe89f08381179aab9d5690e08bc0a3bfaf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.11901",
    "kind": "arxiv",
    "version": 2
  }
}